location

In order to get an idea on the concentration of apartment listings in the area of Copenhagen, we plotted a map showing the number of flat available for rent for 4 nights or less. We used clusters instead of point to make the map more readable and to get a better idea of the number of listings in each area.

# Take the filtered listings with a min of 4 nights and create a map of the apartments in Copenhagen
listings_filtered_4nights %>% 
  leaflet() %>% 
  addProviderTiles("OpenStreetMap.Mapnik") %>% 
  addCircleMarkers(lng = ~longitude, 
                   lat = ~latitude, 
                   radius = 1,
                   fillOpacity = 0.4, 
                   popup = ~listing_url,
                   label = ~property_type,
                   #To get a better overview of the number and location of apartments in Copenhagen, a clustered map was chosen instead of the original point mapping
                   clusterOptions = markerClusterOptions()
                   )

The map shows the number of available flats are located in the city center. The more we get away from the center the fewer the number of flats available.

To gauge the price difference in each area in Copenhagen, we plotted a heatmap showing the more expensive areas in a brighter red colour. Also we plotted a bar chart to get an idea of the median price for each area. The reason for using median over mean is because the listings in Copenhagen have very extreme values and they skew the mean too much for certain areas.

#maps price to seven colors using quantiles
qpal <- colorQuantile("Reds", listings_filtered_4nights$price, n = 7)

listings_filtered_4nights %>% 
leaflet() %>% 
  addProviderTiles("OpenStreetMap.Mapnik") %>% 
  addCircleMarkers(lng = ~longitude, 
                   lat = ~latitude, 
                   radius = 1,
                   fillOpacity = 0.4, 
                   popup = ~listing_url,
                   label = ~property_type,
                   color = ~qpal(price))

We can conclude that the harbour area in Copehagen has the most expensive listings. Therefore we suspect that location will have a high coefficient when we will be running te regression models.

#Calculated median price per night for each neighborhood
median_per_neighborhood <- listings_filtered_4nights %>% 
  group_by(neighbourhood_cleansed) %>% 
  summarise(median_price = median(price))
#Price per night for each neighborhood
median_per_neighborhood %>% 
  ggplot(aes(
    x = reorder(neighbourhood_cleansed, median_price),
    y = median_price
  )) +
    geom_col(fill = "#FF5A5F") +
  scale_fill_manual(values="#FF5A5F")+
  labs(
    title = "Median price per night per neighborhood",
    x = "",
    y = "Median price per neighborhood",
    caption = "Source: Airbnb"
  ) +
  coord_flip() +
  theme_classic() +
  NULL

The Indre By area in Copenhagen is the central harbour area and is the most expensive area for AirBnB prices. This confirms that the neighborhood variable will have a significant impact on the price variable.

accommodation type

Next up, we have plotted a number of bar charts to display the price relationship with the types of accommodation.

Median price per night per property type: The histogram showed that among all the property types, the lowest median price per night is allocated to the appartments

Median price per room type: The histogram showed that hotel rooms are generally more expensive than the other types of rooms available.

# Calculate median price per night for each room type
median_per_proptype <- listings_filtered_4nights %>% 
  group_by(prop_type_simplified) %>% 
  summarise(median_price = median(price))

# Plot a bar chart with median price per night for each property type
median_per_proptype %>% 
  ggplot(aes(
    x = reorder(prop_type_simplified, desc(median_price)),
    y = median_price
  )) +
  geom_col(fill = "#FF5A5F") +
  scale_fill_manual(values="#FF5A5F")+
  labs(
    title = "Median price per night per property type",
    x = "",
    y = "Median price per night",
    caption = "Source: AirBnB"
  ) +
  NULL

# Calculate median price per night for each room type
median_per_roomtype <- listings_filtered_4nights %>% 
  group_by(room_type) %>% 
  summarise(median_price = median(price))

# Price per night for each room type
median_per_roomtype %>% 
  ggplot(aes(
    x = reorder(room_type, desc(median_price)),
    y = median_price
  )) +
  geom_col(fill = "#FF5A5F") +
  scale_fill_manual(values="#FF5A5F")+
  labs(
    title = "Median price per night per room type",
    x = "",
    y = "Median price per night",
    caption = "Source: AirBnB"
  ) +
  NULL

From this we can conclude that both room type and property type have an influence on the price.

rating

Following from this, we wanted to know what influence rating has on the price. For this we used both data on the review scores and whether the listing is posted by a superhost.

#Plotted a density graph to display the relationship with price in being a superhost
listings_clean %>%
  ggplot(aes( x = log(price),
  #colour the graph by being a superhost or not and filtering out the NA values
  colour = !is.na(host_is_superhost))) + 
  geom_density() +    
  labs(      
      title = "Density plot for prices on whether host is superhost",
      x = "price per night (log)",
      y = "density",
      caption = "Source: AirBnB",
      color = "(Non)superhost\n"   ) + 
      theme_classic() + 
  NULL

## Warning: Removed 2 rows containing non-finite values (stat_density).

#Plotted a histogram to display the distribution of ratings and to show if this is affected by being a superhost

listings_clean %>%
  #Filtered out the NA's in superhost
  filter(!is.na(host_is_superhost)) %>% 
  ggplot(aes(
    x = review_scores_rating,
    fill = host_is_superhost
  )) +
  # set the binwidth to 1 to match the scoring bins in the original data
  geom_histogram(binwidth = 1) +
      labs(
      title = "Histogram for review score distribution with (non)superhosts",
      x = "Review scores",
      y = "Count",
      caption = "Source: AirBnB"
    ) +
  #change name of legend
  scale_fill_discrete(
                      name = NULL,
                      labels = c("Non-superhost", "Superhost")
                      ) +
  theme_classic() +
  NULL

## Warning: Removed 5442 rows containing non-finite values (stat_bin).

#plotted a scatter graph showing the relationship between review score and price
listings_clean %>%
  ggplot(aes(
    x = review_scores_rating,
    y = price
  )) +
  geom_point() +
  #Applied a logscale to make the relationship more visible
  scale_y_log10() +
  #Applied a linear line to display any relationship in with price with a higher review score
  geom_smooth(method = lm) +
      labs(
      title = "Scatter plot showing relationship between review scores and price",
      x = "Review scores",
      y = "Price per night (log)",
      caption = "Source: Airbnb"
    ) + 
  theme_classic() +
  NULL

## Warning: Transformation introduced infinite values in continuous y-axis

## Warning: Transformation introduced infinite values in continuous y-axis

## Warning: Removed 5448 rows containing non-finite values (stat_smooth).

## Warning: Removed 5447 rows containing missing values (geom_point).

From this we can conclude that being a superhost does have an influence on the price. People would prefer a superhost, so it seems logical that the average price for a superhost is higher than a listing under a normal host. The ratings however don’t seem to be related to being a superhost. In fact the perfect scores are more among non-superhosts. This could be because of the higher expectations set by booking via a superhost, this could make guests more critical when writing a review. finally, there does not seem to be a strong correlation with a rating score and the price. Hosts will not alter their prices to their review scores.

GGpairs

To display a comprehensive overview of the correlation between variables and the price we plotted a GGpairs plot. Using all the selected variables.

# Display the correlation between four important variables

listings_clean %>%
  select(price, review_scores_rating, bedrooms, bathrooms, accommodates) %>% 
  ggpairs(cardinality_threshold=NULL)

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 5447 rows containing missing values

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 29 rows containing missing values

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 12 rows containing missing values

## Warning: Removed 5447 rows containing missing values (geom_point).

## Warning: Removed 5447 rows containing non-finite values (stat_density).

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 5458 rows containing missing values

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 5454 rows containing missing values

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 5447 rows containing missing values

## Warning: Removed 29 rows containing missing values (geom_point).

## Warning: Removed 5458 rows containing missing values (geom_point).

## Warning: Removed 29 rows containing non-finite values (stat_density).

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 38 rows containing missing values

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 29 rows containing missing values

## Warning: Removed 12 rows containing missing values (geom_point).

## Warning: Removed 5454 rows containing missing values (geom_point).

## Warning: Removed 38 rows containing missing values (geom_point).

## Warning: Removed 12 rows containing non-finite values (stat_density).

## Warning in ggally_statistic(data = data, mapping = mapping, na.rm = na.rm, :
## Removed 12 rows containing missing values

## Warning: Removed 5447 rows containing missing values (geom_point).

## Warning: Removed 29 rows containing missing values (geom_point).

## Warning: Removed 12 rows containing missing values (geom_point).

# Create new variable for 4 nights using price, guests_included, cleaning_fee and extra_people
listings_new <- listings_clean %>%
  mutate(price_4_nights = ifelse(
    guests_included <= 1,
    (price + extra_people) * 4 + cleaning_fee,
    (price) * 4 + cleaning_fee
  ))

# Density plots for price_4_nights
density.default(listings_new$price_4_nights)

## 
## Call:
##  density.default(x = listings_new$price_4_nights)
## 
## Data: listings_new$price_4_nights (28523 obs.);  Bandwidth 'bw' = 173
## 
##        x                  y            
##  Min.   :  -518.9   Min.   :0.000e+00  
##  1st Qu.: 68915.5   1st Qu.:0.000e+00  
##  Median :138350.0   Median :0.000e+00  
##  Mean   :138350.0   Mean   :4.589e-06  
##  3rd Qu.:207784.5   3rd Qu.:2.000e-10  
##  Max.   :277218.9   Max.   :3.565e-04

# Calculate the most frequently occurring price (mode) for 4 nights 
max_p4n <- density(listings_new$price_4_nights)$x[which.max(density(listings_new$price_4_nights)$y)]
max_p4n

## [1] 2742.17

# Plot density of price_4_nights
ggplot(
  listings_new,
  aes(x = price_4_nights)) +
  geom_density() +
  # Plot vertical line to show maximum value
  geom_vline(xintercept =  max_p4n) +
  theme_classic() +
  NULL

# Plot density of log(price_4_nights)
ggplot(listings_new, aes(x = log(price_4_nights))) +
  geom_density() +
  theme_classic() +
  NULL

## Warning: Removed 1 rows containing non-finite values (stat_density).

Model 1

Fitting a regression model called model1 with the following explanatory variables: prop_type_simplified, number_of_reviews, and review_scores_rating

# Create a new dataset with the new variable of log(price_4_nights)
listings_log <- listings_new %>%
  mutate(price_4_nights_log = log10(price_4_nights)) 
  
# Create model1 of price_4_nights with explanatory variables prop_type_simplified, number_of_reviews and review_scores_ratings
model1 <- lm(price_4_nights_log ~
             prop_type_simplified +
             number_of_reviews +
             review_scores_rating,
             data = listings_log
             )

model1 %>% tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.24	0.0198	164	0	3.21	3.28
prop_type_simplifiedCondominium	0.033	0.00576	5.74	9.66e-09	0.0218	0.0443
prop_type_simplifiedHouse	0.119	0.00693	17.1	4.35e-65	0.105	0.132
prop_type_simplifiedOther	0.178	0.00872	20.4	1.7e-91	0.161	0.195
prop_type_simplifiedTownhouse	0.177	0.0102	17.4	2.2e-67	0.157	0.197
number_of_reviews	0.000188	4.84e-05	3.89	0.000101	9.34e-05	0.000283
review_scores_rating	0.00235	0.000207	11.3	9.89e-30	0.00194	0.00276

model1 %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.046	0.0457	0.215	185	3.13e-231	6	2.77e+03	-5.53e+03	-5.46e+03	1.06e+03	23069	23076

# Check residuals
autoplot(model1)

## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

Ratings (review_scores_rating) is a significant predictor. Controlling for other variables, every 1 point increase in rating is associated with $ 0.002 increase in log10(price_4_nights).

Interpretation of prop_type_simplified predictor:

Property type (prop_type_simplified) is a significant predictor. Controlling for other variables, switching property type from apartment to condomunium would result in 0.034 increase in log10(price_4_nights). Similarly, switching property type from apartment to house would result in 0.11 increase in log10(price_4_nights); switching property type from apartment to townhouse would result in 0.17 increase in log10(price_4_nights); switching property type from apartment to property types other than the aforementioned 3 types would result in an average of 0.18 increase in log10(price_4_nights).

Model 1: 4%

Model 2

We want to determine if room_type is a significant predictor of the cost for 4 nights, given everything else in the model.

# Create model2 by adding room_type to model1
model2 <- lm(price_4_nights_log ~
             prop_type_simplified +
             number_of_reviews +
             review_scores_rating +
             room_type, 
             data = listings_log
             )

model2 %>% tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.36	0.0177	189	0	3.32	3.39
prop_type_simplifiedCondominium	0.0168	0.00513	3.27	0.00107	0.00674	0.0269
prop_type_simplifiedHouse	0.126	0.00618	20.4	1.8e-91	0.114	0.138
prop_type_simplifiedOther	0.168	0.00797	21.1	1.14e-97	0.152	0.184
prop_type_simplifiedTownhouse	0.166	0.00905	18.3	1.98e-74	0.148	0.184
number_of_reviews	0.000668	4.36e-05	15.3	1.33e-52	0.000582	0.000753
review_scores_rating	0.00154	0.000185	8.33	8.6e-17	0.00118	0.00191
room_typeHotel room	0.112	0.0342	3.28	0.00104	0.0452	0.179
room_typePrivate room	-0.271	0.00355	-76.3	0	-0.278	-0.264
room_typeShared room	-0.362	0.0246	-14.7	5.51e-49	-0.41	-0.314

model2 %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.243	0.243	0.191	823	0	9	5.44e+03	-1.09e+04	-1.08e+04	843	23066	23076

# Check residuals
autoplot(model2)

Interpretation of room_type predictor:

The result of model2 regression shows that rooms_type is a significant predictor. Controlling for other variables, switching room type from entire house to hotel room would result in 0.11 increase in log10(price_4_nights). Nevertheless, switching from entire house to private room would result in 0.27 drop in log10(price_4_nights); switching from entire house to shared room would result in 0.38 drop in log10(price_4_nights).

Model 2: 24%

Model 3

Are the number of bathrooms, bedrooms, beds, or size of the house (accomodates) significant predictors of price_4_nights?

# Create model3a by adding bathrooms, bedrooms, beds, accommodates to model2 
model3a<-lm(price_4_nights_log ~
            prop_type_simplified +
             number_of_reviews +
             review_scores_rating +
             room_type + 
             bathrooms +
             bedrooms +
             beds + 
             accommodates, 
            data = listings_log)

model3a %>% 
  tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.08	0.0163	189	0	3.05	3.12
prop_type_simplifiedCondominium	0.0105	0.00452	2.31	0.0207	0.0016	0.0193
prop_type_simplifiedHouse	-0.0476	0.00594	-8.02	1.08e-15	-0.0593	-0.036
prop_type_simplifiedOther	0.0906	0.00709	12.8	2.97e-37	0.0767	0.105
prop_type_simplifiedTownhouse	0.00279	0.00835	0.334	0.738	-0.0136	0.0191
number_of_reviews	0.000596	3.85e-05	15.5	7.78e-54	0.000521	0.000672
review_scores_rating	0.00166	0.000164	10.2	3.24e-24	0.00134	0.00199
room_typeHotel room	0.223	0.0302	7.38	1.65e-13	0.164	0.282
room_typePrivate room	-0.18	0.00338	-53.2	0	-0.187	-0.174
room_typeShared room	-0.261	0.0217	-12	3e-33	-0.303	-0.218
bathrooms	0.0581	0.0047	12.4	4.54e-35	0.0489	0.0673
bedrooms	0.0501	0.00224	22.3	1.83e-109	0.0457	0.0545
beds	-0.00273	0.00125	-2.19	0.0283	-0.00517	-0.00029
accommodates	0.0389	0.00131	29.6	2.69e-189	0.0363	0.0415

model3a %>%
  glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.412	0.412	0.168	1.24e+03	0	13	8.36e+03	-1.67e+04	-1.66e+04	653	23021	23035

# Test VIF
car::vif(model3a)

##                          GVIF Df GVIF^(1/(2*Df))
## prop_type_simplified 1.373951  4        1.040510
## number_of_reviews    1.029840  1        1.014810
## review_scores_rating 1.012554  1        1.006257
## room_type            1.272593  3        1.040994
## bathrooms            1.332643  1        1.154401
## bedrooms             3.071499  1        1.752569
## beds                 2.550304  1        1.596967
## accommodates         3.628682  1        1.904910

# Check residuals
autoplot(model3a)

The number of bathrooms, bedrooms and size of the house (accommodates) are significant predictors of log10(price_4_nights) and are all positively related with price_4_nights, while number of beds is not a significant predictor. Coefficients show that each additional bathroom is associated with 0.06 increase in log10(price_4_nights); each additional bedroom is associated with 0.05 increase in log10(price_4_nights). There might be a problem with multi-collinearity since intuitively the number of bathrooms and bedrooms should have a positive relationship with size of the house. A further analysis on VIF shows that size of the house has slight correlation with other predictors but is within an acceptable range.

# Create model3 by removing beds from model3a 
model3<-lm(price_4_nights_log ~
           prop_type_simplified +
           number_of_reviews +
           review_scores_rating +
           room_type + 
           bathrooms +
           bedrooms +
           accommodates, 
           data = listings_log
           )

model3 %>% tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.08	0.0163	189	0	3.05	3.12
prop_type_simplifiedCondominium	0.0106	0.00452	2.34	0.0195	0.0017	0.0194
prop_type_simplifiedHouse	-0.0481	0.00593	-8.11	5.24e-16	-0.0598	-0.0365
prop_type_simplifiedOther	0.0905	0.00709	12.7	4.17e-37	0.0766	0.104
prop_type_simplifiedTownhouse	0.00227	0.00834	0.273	0.785	-0.0141	0.0186
number_of_reviews	0.000598	3.85e-05	15.5	3.5e-54	0.000523	0.000674
review_scores_rating	0.00167	0.000164	10.2	1.7e-24	0.00135	0.00199
room_typeHotel room	0.223	0.0302	7.39	1.58e-13	0.164	0.282
room_typePrivate room	-0.181	0.00338	-53.5	0	-0.187	-0.174
room_typeShared room	-0.262	0.0217	-12.1	1.91e-33	-0.304	-0.219
bathrooms	0.0581	0.0047	12.4	4.75e-35	0.0489	0.0673
bedrooms	0.0488	0.00216	22.6	1.72e-111	0.0446	0.0531
accommodates	0.0376	0.00118	31.9	1.11e-218	0.0353	0.0399

model3 %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.413	0.412	0.168	1.35e+03	0	12	8.36e+03	-1.67e+04	-1.66e+04	654	23047	23060

# Test VIF
car::vif(model3)

##                          GVIF Df GVIF^(1/(2*Df))
## prop_type_simplified 1.370590  4        1.040192
## number_of_reviews    1.029562  1        1.014673
## review_scores_rating 1.011882  1        1.005924
## room_type            1.271896  3        1.040899
## bathrooms            1.332684  1        1.154419
## bedrooms             2.862720  1        1.691957
## accommodates         2.929976  1        1.711717

# Check residuals
autoplot(model3)

Model 3: 41%

Model 4

Do superhosts command a pricing premium, after controlling for other variables?

# Create model4 by adding host_is_superhost to model3
model4<-lm(price_4_nights_log ~
             prop_type_simplified +
             number_of_reviews +
             review_scores_rating +
             room_type + 
             bathrooms +
             bedrooms +
             accommodates +
             host_is_superhost,
            data = listings_log
           )
model4 %>% tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.1	0.0164	189	0	3.07	3.13
prop_type_simplifiedCondominium	0.00988	0.00452	2.19	0.0287	0.00103	0.0187
prop_type_simplifiedHouse	-0.0478	0.00592	-8.07	7.47e-16	-0.0594	-0.0362
prop_type_simplifiedOther	0.089	0.00708	12.6	4.07e-36	0.0751	0.103
prop_type_simplifiedTownhouse	0.00141	0.00833	0.17	0.865	-0.0149	0.0177
number_of_reviews	0.000484	4.01e-05	12.1	2.24e-33	0.000405	0.000562
review_scores_rating	0.00145	0.000165	8.81	1.28e-18	0.00113	0.00178
room_typeHotel room	0.226	0.0301	7.49	6.91e-14	0.167	0.285
room_typePrivate room	-0.183	0.00338	-54.1	0	-0.189	-0.176
room_typeShared room	-0.261	0.0216	-12.1	2.06e-33	-0.304	-0.219
bathrooms	0.0582	0.00469	12.4	3.14e-35	0.049	0.0673
bedrooms	0.0491	0.00216	22.7	2.89e-113	0.0449	0.0534
accommodates	0.0374	0.00118	31.8	9.41e-217	0.0351	0.0397
host_is_superhostTRUE	0.0354	0.00358	9.88	5.54e-23	0.0284	0.0424

model4 %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.415	0.415	0.168	1.26e+03	0	13	8.4e+03	-1.68e+04	-1.67e+04	651	23040	23054

# Test VIF
car::vif(model4)

##                          GVIF Df GVIF^(1/(2*Df))
## prop_type_simplified 1.371707  4        1.040298
## number_of_reviews    1.122623  1        1.059539
## review_scores_rating 1.028858  1        1.014326
## room_type            1.277660  3        1.041684
## bathrooms            1.332709  1        1.154430
## bedrooms             2.863006  1        1.692042
## accommodates         2.930492  1        1.711868
## host_is_superhost    1.122152  1        1.059317

# Check residuals
autoplot(model4)

Interpretation of superhost predictor:

Since the p-value for the estimate of the superhost coefficient is significant (with a p-value of 0.36 and a t-statistic of 0.9), it seems that superhosts do command a price premium from their guests in Copenhagen. Compared to non-superhost, being a superhost is associated with 0.04 increase in log10(price_4_nights).

Since the p-value for the estimate of the superhost coefficient is significant (with a p-value of 0.36 and a t-statistic of 0.9), it seems that superhosts do command a price premium from their guests in Copenhagen. Compared to non-superhost, being a superhost is associated with 0.03 increase in log10(price_4_nights).

# Create model4b by adding host_is_superhost to model4 and create an interaction variable 
model4b<-lm(price_4_nights_log ~
            prop_type_simplified +
             number_of_reviews +
             review_scores_rating +
             room_type + 
             bathrooms +
             bedrooms +
             accommodates +
             host_is_superhost +
             host_is_superhost*review_scores_rating,
             data = listings_log
            )
model4b %>% tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.11	0.0165	188	0	3.07	3.14
prop_type_simplifiedCondominium	0.00979	0.00452	2.17	0.0301	0.000945	0.0186
prop_type_simplifiedHouse	-0.0477	0.00592	-8.06	8.12e-16	-0.0593	-0.0361
prop_type_simplifiedOther	0.0891	0.00708	12.6	3.59e-36	0.0752	0.103
prop_type_simplifiedTownhouse	0.0015	0.00833	0.18	0.857	-0.0148	0.0178
number_of_reviews	0.000489	4.02e-05	12.2	5.72e-34	0.00041	0.000568
review_scores_rating	0.00141	0.000166	8.45	3.12e-17	0.00108	0.00173
room_typeHotel room	0.228	0.0301	7.55	4.39e-14	0.169	0.287
room_typePrivate room	-0.183	0.00338	-54.1	0	-0.19	-0.176
room_typeShared room	-0.261	0.0216	-12.1	1.78e-33	-0.304	-0.219
bathrooms	0.058	0.00469	12.4	5.16e-35	0.0488	0.0672
bedrooms	0.0491	0.00216	22.7	2.95e-113	0.0449	0.0534
accommodates	0.0374	0.00118	31.8	5.54e-217	0.0351	0.0397
host_is_superhostTRUE	-0.242	0.122	-1.99	0.0471	-0.481	-0.00306
review_scores_rating:host_is_superhostTRUE	0.00285	0.00125	2.28	0.0228	0.000396	0.0053

model4b %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.415	0.415	0.168	1.17e+03	0	14	8.41e+03	-1.68e+04	-1.67e+04	651	23039	23054

# Test VIF
car::vif(model4b)

##                                               GVIF Df GVIF^(1/(2*Df))
## prop_type_simplified                      1.371877  4        1.040314
## number_of_reviews                         1.126391  1        1.061316
## review_scores_rating                      1.046224  1        1.022851
## room_type                                 1.278764  3        1.041834
## bathrooms                                 1.333108  1        1.154603
## bedrooms                                  2.863011  1        1.692043
## accommodates                              2.930623  1        1.711906
## host_is_superhost                      1301.822960  1       36.080784
## review_scores_rating:host_is_superhost 1301.627193  1       36.078071

# Check residuals
autoplot(model4b)

Interaction variable host_is_superhost*review_scores_rating is not significant, therefore we do not include it.

Model 4: 41%

Model 5

Most owners advertise the exact location of their listing (is_location_exact == TRUE), while a non-trivial proportion don’t. After controlling for other variables, is a listing’s exact location a significant predictor of price_4_nights?

# Create model5 by adding is_location_exact == TRUE to model4
model5<-lm(price_4_nights_log ~
             prop_type_simplified +
             number_of_reviews +
             review_scores_rating +
             room_type +
             bathrooms +
             bedrooms +
             accommodates +
             host_is_superhost +
             is_location_exact,
             data = listings_log
           )
model5 %>% tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.11	0.0165	188	0	3.07	3.14
prop_type_simplifiedCondominium	0.00975	0.00452	2.16	0.0308	0.000903	0.0186
prop_type_simplifiedHouse	-0.0478	0.00592	-8.07	7.27e-16	-0.0594	-0.0362
prop_type_simplifiedOther	0.0884	0.00709	12.5	1.36e-35	0.0745	0.102
prop_type_simplifiedTownhouse	0.00103	0.00833	0.123	0.902	-0.0153	0.0174
number_of_reviews	0.000485	4.01e-05	12.1	1.71e-33	0.000406	0.000563
review_scores_rating	0.00146	0.000165	8.85	9.22e-19	0.00114	0.00178
room_typeHotel room	0.227	0.0301	7.52	5.6e-14	0.168	0.286
room_typePrivate room	-0.183	0.00338	-54.1	0	-0.19	-0.176
room_typeShared room	-0.261	0.0216	-12.1	2.35e-33	-0.303	-0.218
bathrooms	0.0582	0.00469	12.4	2.72e-35	0.049	0.0674
bedrooms	0.0491	0.00216	22.7	2.79e-113	0.0449	0.0534
accommodates	0.0374	0.00118	31.8	3.56e-217	0.0351	0.0397
host_is_superhostTRUE	0.0356	0.00358	9.95	2.93e-23	0.0286	0.0426
is_location_exactTRUE	-0.00547	0.00277	-1.97	0.0484	-0.0109	-3.73e-05

model5 %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.415	0.415	0.168	1.17e+03	0	14	8.41e+03	-1.68e+04	-1.67e+04	651	23039	23054

# Test VIF
car::vif(model5)

##                          GVIF Df GVIF^(1/(2*Df))
## prop_type_simplified 1.375094  4        1.040619
## number_of_reviews    1.122768  1        1.059607
## review_scores_rating 1.029247  1        1.014518
## room_type            1.278044  3        1.041736
## bathrooms            1.332750  1        1.154448
## bedrooms             2.863006  1        1.692042
## accommodates         2.931407  1        1.712135
## host_is_superhost    1.123547  1        1.059975
## is_location_exact    1.005398  1        1.002695

# Check residuals
autoplot(model5)

A listing’s exact location variable has a p value of 0.34, and therefore is not a significant predictor of price_4_nights. Thus, we will not include it in the following models.

Model 4: 41%

Model 6

In order to reduce the number of neighbourhoods for our analysis we cluster the different neighbourhoods into groups, based on our experience, talking to locals, and research.

The city of Copenhagen has 10 official administrative districts. Additionally, there is Frederiksberg, which is an independent municipality and, thus, separate from the Copenhagen Municipality, however, it is still part of Copenhagen city.

Indre By is the city center of Copenhagen and will remain its own cluster “Center”.

All the residential neighbourhoods surrounding the city center are commonly grouped together, and since they all end in -bro, often referred to as -bro districts (Brokvaterer in Danish). Frederiksberg is often also included in the -bro districts. Hence, we will cluster these 4 Brokvaterer districts into one group of Brokvarterer

Additionally, the two Amager districts (Vest and Ost) are grouped together.

In the West, Valby, Vanlose and Brønshøj-Husum are summarized.

Lastly, Bispebjerg, often referred to as Nordvest, which is more of a residential neighbourhood, is its own cluster.

# Create variable neighbourhood_simplified with 5 categories 
listings_log <- listings_log %>%
  mutate(neighbourhood_simplified = case_when(
    neighbourhood_cleansed %in% c("Indre By") ~ "Center",
    neighbourhood_cleansed %in% c("Frederiksberg","Nrrebro", "sterbro","Vesterbro-Kongens Enghave") ~ "Brokvarterer", 
    neighbourhood_cleansed %in% c("Amager st","Amager Vest") ~ "Amager",
    neighbourhood_cleansed %in% c("Brnshj-Husum","Valby", "Vanlose") ~ "West",
    TRUE ~ "Nordvest"
  ))

# Create model6 by adding neighbourhood_simplified to model3
model6<-lm(price_4_nights_log ~
            prop_type_simplified +
             number_of_reviews +
             review_scores_rating +
             room_type +
             bathrooms +
             bedrooms +
             accommodates +
             neighbourhood_simplified +
             host_is_superhost+
             NULL,
             data = listings_log
           )
model6 %>% tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.1	0.0154	202	0	3.07	3.13
prop_type_simplifiedCondominium	0.0143	0.00418	3.42	0.000622	0.00611	0.0225
prop_type_simplifiedHouse	0.0189	0.0057	3.32	0.000915	0.00773	0.0301
prop_type_simplifiedOther	0.091	0.00657	13.9	1.83e-43	0.0781	0.104
prop_type_simplifiedTownhouse	0.0141	0.00775	1.82	0.0689	-0.00109	0.0293
number_of_reviews	0.000231	3.73e-05	6.2	5.92e-10	0.000158	0.000304
review_scores_rating	0.00132	0.000153	8.61	7.6e-18	0.00102	0.00162
room_typeHotel room	0.139	0.0279	4.97	6.9e-07	0.0839	0.193
room_typePrivate room	-0.175	0.00313	-55.9	0	-0.181	-0.169
room_typeShared room	-0.246	0.02	-12.3	1.46e-34	-0.285	-0.207
bathrooms	0.0541	0.00434	12.5	1.51e-35	0.0456	0.0626
bedrooms	0.0466	0.002	23.3	1.26e-118	0.0427	0.0505
accommodates	0.0364	0.00109	33.4	1.2e-238	0.0343	0.0385
neighbourhood_simplifiedBrokvarterer	0.0274	0.00295	9.29	1.63e-20	0.0216	0.0331
neighbourhood_simplifiedCenter	0.161	0.00383	42.1	0	0.154	0.169
neighbourhood_simplifiedNordvest	-0.0911	0.00451	-20.2	3.76e-90	-0.0999	-0.0823
neighbourhood_simplifiedWest	-0.0836	0.005	-16.7	1.71e-62	-0.0934	-0.0738
host_is_superhostTRUE	0.0311	0.00331	9.4	5.85e-21	0.0246	0.0376

model6 %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.5	0.499	0.155	1.35e+03	0	17	1.02e+04	-2.04e+04	-2.02e+04	557	23036	23054

# Test VIF
car::vif(model6)

##                              GVIF Df GVIF^(1/(2*Df))
## prop_type_simplified     1.501568  4        1.052127
## number_of_reviews        1.136203  1        1.065928
## review_scores_rating     1.030892  1        1.015329
## room_type                1.286594  3        1.042894
## bathrooms                1.333482  1        1.154765
## bedrooms                 2.867499  1        1.693369
## accommodates             2.937274  1        1.713848
## neighbourhood_simplified 1.151978  4        1.017842
## host_is_superhost        1.123124  1        1.059775

# Check residuals
autoplot(model6)

One can see that the neighbourhood of an apartment is an predictor of the price for 4 nights in Copenhagen.

Interpretation of neighbourhood predictor:

We can see that all the neighbourhood variables are significant predictors of the price for 4 nights in Copenhagen. Taking Amager as the base, Brokvarterer is asscociated with 0.03 more in log10(price_4_nights); Center is asscociated with 0.16 more in log10(price_4_nights); Nordvest is asscociated with 0.09 drop in log10(price_4_nights); West is asscociated with 0.09 drop in log10(price_4_nights).

Model 6: 50%

Model 7

What is the effect of cancellation_policy on price_4_nights, after we control for other variables?

# Create model7 by adding cancellation_policy to model6
model7<-lm(price_4_nights_log ~
            prop_type_simplified +
             number_of_reviews +
             review_scores_rating +
             room_type +
             bathrooms +
             bedrooms +
             accommodates +
             neighbourhood_simplified +
             cancellation_policy+
             host_is_superhost+NULL,
             data = listings_log
           )
model7 %>% tidy(conf.int=TRUE)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	3.09	0.0153	202	0	3.06	3.12
prop_type_simplifiedCondominium	0.0124	0.00415	2.99	0.00284	0.00425	0.0205
prop_type_simplifiedHouse	0.0189	0.00566	3.35	0.000822	0.00784	0.03
prop_type_simplifiedOther	0.0734	0.00712	10.3	6.64e-25	0.0595	0.0874
prop_type_simplifiedTownhouse	0.0125	0.0077	1.63	0.104	-0.00257	0.0276
number_of_reviews	0.00017	3.73e-05	4.57	4.99e-06	9.73e-05	0.000244
review_scores_rating	0.00131	0.000152	8.61	7.72e-18	0.00101	0.00161
room_typeHotel room	0.175	0.0279	6.29	3.18e-10	0.121	0.23
room_typePrivate room	-0.17	0.00312	-54.7	0	-0.177	-0.164
room_typeShared room	-0.244	0.0199	-12.3	1.19e-34	-0.283	-0.206
bathrooms	0.0532	0.00431	12.3	7.16e-35	0.0447	0.0616
bedrooms	0.0455	0.00199	22.9	1.16e-114	0.0416	0.0494
accommodates	0.0359	0.00108	33.2	1.05e-235	0.0338	0.038
neighbourhood_simplifiedBrokvarterer	0.0266	0.00292	9.11	9.1e-20	0.0209	0.0324
neighbourhood_simplifiedCenter	0.158	0.00381	41.5	0	0.151	0.166
neighbourhood_simplifiedNordvest	-0.0898	0.00447	-20.1	5.59e-89	-0.0986	-0.0811
neighbourhood_simplifiedWest	-0.0805	0.00496	-16.2	6.35e-59	-0.0903	-0.0708
cancellation_policymoderate	0.0269	0.00241	11.2	7.93e-29	0.0222	0.0316
cancellation_policystrict_14_with_grace_period	0.0457	0.00262	17.4	9.54e-68	0.0405	0.0508
cancellation_policysuper_strict_60	0.127	0.0173	7.36	1.88e-13	0.0935	0.161
host_is_superhostTRUE	0.0294	0.00329	8.94	4.11e-19	0.023	0.0359

model7 %>% glance()

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.507	0.507	0.154	1.19e+03	0	20	1.04e+04	-2.07e+04	-2.05e+04	548	23033	23054

# Test VIF
car::vif(model7)

##                              GVIF Df GVIF^(1/(2*Df))
## prop_type_simplified     1.793107  4        1.075724
## number_of_reviews        1.153751  1        1.074128
## review_scores_rating     1.037877  1        1.018762
## room_type                1.312570  3        1.046374
## bathrooms                1.335585  1        1.155675
## bedrooms                 2.871572  1        1.694571
## accommodates             2.943557  1        1.715680
## neighbourhood_simplified 1.161450  4        1.018885
## cancellation_policy      1.268876  3        1.040487
## host_is_superhost        1.124756  1        1.060545

# Check residuals
autoplot(model7)

The cancellation policy is a significant predictor on price, with a flexible policy commanding the lowest price and with a strict policy commanding the highest price. This is surprising since usually hosts should be rewarded for the risk that they are taking with a flexible cancellation policy. On the other hand, usually expensive and nice places have a stricter cancellation policy since the cost of having the place empty for a night is relatively higher. Thus, in the end the cancellation policy might rather be a consequence of the price and not a predictor of it.

Model 7: 51%

final_model <- lm(price_4_nights_log ~
                  prop_type_simplified +
                  number_of_reviews +
                  review_scores_rating +
                  room_type +
                  bathrooms +
                  bedrooms +
                  accommodates +
                  neighbourhood_simplified +
                  cancellation_policy
                  +host_is_superhost,
                  data = listings_log
                  )

mosaic::msummary(final_model)

##                                                  Estimate Std. Error t value
## (Intercept)                                     3.086e+00  1.530e-02 201.705
## prop_type_simplifiedCondominium                 1.239e-02  4.149e-03   2.985
## prop_type_simplifiedHouse                       1.893e-02  5.658e-03   3.346
## prop_type_simplifiedOther                       7.342e-02  7.116e-03  10.318
## prop_type_simplifiedTownhouse                   1.251e-02  7.695e-03   1.626
## number_of_reviews                               1.705e-04  3.733e-05   4.566
## review_scores_rating                            1.310e-03  1.522e-04   8.611
## room_typeHotel room                             1.755e-01  2.789e-02   6.293
## room_typePrivate room                          -1.705e-01  3.118e-03 -54.671
## room_typeShared room                           -2.445e-01  1.988e-02 -12.298
## bathrooms                                       5.315e-02  4.308e-03  12.339
## bedrooms                                        4.547e-02  1.987e-03  22.888
## accommodates                                    3.592e-02  1.083e-03  33.169
## neighbourhood_simplifiedBrokvarterer            2.663e-02  2.924e-03   9.107
## neighbourhood_simplifiedCenter                  1.581e-01  3.813e-03  41.464
## neighbourhood_simplifiedNordvest               -8.984e-02  4.472e-03 -20.087
## neighbourhood_simplifiedWest                   -8.053e-02  4.961e-03 -16.232
## cancellation_policymoderate                     2.692e-02  2.413e-03  11.156
## cancellation_policystrict_14_with_grace_period  4.567e-02  2.617e-03  17.449
## cancellation_policysuper_strict_60              1.274e-01  1.730e-02   7.361
## host_is_superhostTRUE                           2.941e-02  3.289e-03   8.942
##                                                Pr(>|t|)    
## (Intercept)                                     < 2e-16 ***
## prop_type_simplifiedCondominium                0.002838 ** 
## prop_type_simplifiedHouse                      0.000822 ***
## prop_type_simplifiedOther                       < 2e-16 ***
## prop_type_simplifiedTownhouse                  0.103997    
## number_of_reviews                              4.99e-06 ***
## review_scores_rating                            < 2e-16 ***
## room_typeHotel room                            3.18e-10 ***
## room_typePrivate room                           < 2e-16 ***
## room_typeShared room                            < 2e-16 ***
## bathrooms                                       < 2e-16 ***
## bedrooms                                        < 2e-16 ***
## accommodates                                    < 2e-16 ***
## neighbourhood_simplifiedBrokvarterer            < 2e-16 ***
## neighbourhood_simplifiedCenter                  < 2e-16 ***
## neighbourhood_simplifiedNordvest                < 2e-16 ***
## neighbourhood_simplifiedWest                    < 2e-16 ***
## cancellation_policymoderate                     < 2e-16 ***
## cancellation_policystrict_14_with_grace_period  < 2e-16 ***
## cancellation_policysuper_strict_60             1.88e-13 ***
## host_is_superhostTRUE                           < 2e-16 ***
## 
## Residual standard error: 0.1543 on 23033 degrees of freedom
##   (5469 observations deleted due to missingness)
## Multiple R-squared:  0.5072, Adjusted R-squared:  0.5068 
## F-statistic:  1185 on 20 and 23033 DF,  p-value: < 2.2e-16

get_regression_table(final_model)

get_regression_summaries(final_model)

vif(final_model)

##                              GVIF Df GVIF^(1/(2*Df))
## prop_type_simplified     1.793107  4        1.075724
## number_of_reviews        1.153751  1        1.074128
## review_scores_rating     1.037877  1        1.018762
## room_type                1.312570  3        1.046374
## bathrooms                1.335585  1        1.155675
## bedrooms                 2.871572  1        1.694571
## accommodates             2.943557  1        1.715680
## neighbourhood_simplified 1.161450  4        1.018885
## cancellation_policy      1.268876  3        1.040487
## host_is_superhost        1.124756  1        1.060545

Analysis of Coefficients in Final Model

• Property Type Apartments have the lowest price. Compared to an apartment, a town house has a 1.2% higher price, a house a 1.9% higher price and a condominium a 1.2% higher price.“Other” property types have a 7.6% higher price than apartments, which makes sense since it includes special properties such as house boats etc.

• Number of Reviews Already one additional review on AirBnB increases the price of the place 0.02%

• Review_scores_rating For every increase in the review score rating, the price rises by 0.13%

• Room Type A shared room and private room will have the lowest prices, with 21.69% and 15.6% respectively less than an entire home. This is intuitive since you have to share rooms and/or share facilities, such as bathroom and kitchen with other people. Hotel rooms have the highest price with around 19% more than an entire home.

• Bathrooms & Bedrooms The number of bathrooms and bedrooms also have an influence on the price. An additional bathroom will increase the price by 5.4% and an additional bedroom by 4.6%. (both by roughly 5%).

• Accommodates Offering an additional accommodate rises the price by 3.6%

• Superhost Being a super host can increase your price by 2.7%, so it might be worth it to make to superhost!

• Neighbourhoods Looking at the neighbourhoods, we can also see clear trends there. Highest prices are found in the center, which is the case in most cities. There are 17.2% higher than in Amager. Prices in Brokvarterer are 2.7% higher than in Amager. The lowest prices are in Nordvest and the West (8.6% and 7.7% lower than in Amager), which are more residential areas.

• Cancellation Policy Places with flexible cancellation policies have the lowest prices, those with moderate ones are 2.7% higher and those with strict ones 4.9%. The super strict ones have the highest prices with 13.5%

• In conclusion, this model can help AirBnB hosts understand what drives AirBnB prices, e.g. which in neighborhoods one can demand higher prices, and learn which features customer accept to pay more for .